These top attractions in Rome require pre-purchased, timed-entry tickets to avoid long ticket queues: the Colosseum, the Vatican Museums and Galleria Borghese. There are no advance "open" tickets for these 3 venues. By "open" I mean being able to enter at any day or hour with a pre-purchased ticket. You must choose a specific day and open time slot on each attraction's ticketing site.
David, I've no idea what sort of tickets you had but I haven't heard of anyone with pre-purchased tickets from the Vatican's website spending 2 hours in a queue. Your tickets should have been timed-entry so a short shuffle through the security queue. And yes, parts of the museums are very, very crowded. They're the #1 or #2 attraction in Rome and so early-entrance tours and Friday night late openings (in season) have become rather popular ways to try and enjoy the more heavily-visited sections without being overrun.
Editing to add: Sandi, let us know if you don't have links to the official websites for the other 2 attractions mentioned above, OK?